Method and apparatus for generating a three-dimensional model of a region of interest using an imaging system

ABSTRACT

A method of generating a three-dimensional representation of a region of interest on a target object in an x-ray imaging system. The method uses a fiducial marker of known geometry. The region of interest and the fiducial marker are imaged in a plurality of predetermined positions. Expected images of the fiducial marker for each predetermined position are calculated and compared to captured images of the fiducial marker at each predetermined position. The difference between expected and captured imaged is used to generate corrected images of the region of interest for each predetermined position and these corrected images are used to generate a three-dimensional model of the region of interest. The method allows for the generation of useful three-dimensional models of a region of interest in an x-ray imaging system without requiring an expensive mechanical positioning system.

This application is a continuation of U.S. application Ser. No.13/646,965, filed Oct. 8, 2012 (pending) which claims priority toEuropean Application Serial No. 11250872.6 filed Oct. 27, 2011(pending), the disclosures of which are hereby incorporated by referenceherein.

FIELD OF THE INVENTION

The invention relates to an imaging system that is configured togenerate a three-dimensional model of a region of interest of a targetobject using a plurality of two-dimensional images. More particularly,the invention relates to an X-ray imaging system that uses fiducialmarkers of known geometry to allow a high quality three-dimensionalmodel to be obtained using inexpensive imaging equipment.

BACKGROUND TO THE INVENTION

It is necessary to inspect circuit components and their mountings tocheck for the presence of defects or in order to determine the cause ofthe defects. One known technique for inspecting the internal structureof integrated circuit components and their mountings onto printedcircuit boards is X-ray imaging. X-rays from an X-ray source are passedthrough a region of interest on a circuit board and the resulting X-rayimage or projection is detected by an X-ray detector on the oppositeside of the circuit board to the X-ray source. This produces atwo-dimensional image or slice through the region of interest. The X-raysource produces X-rays of sufficient energy to pass through the regionof interest while also having a low enough energy to produce significantcontrast within the resulting image.

This two-dimensional imaging technique is effective but often providesinsufficient information. For example, there may be objects that occludethe desired view through the region of interest or it may simply be thatthe region of interest is sufficiently complicated to require review inthree dimensions. The region of interest may be all or only part of acomponent, or may be several components.

Three-dimensional models of regions of interest can be obtained bycombining multiple two-dimensional images taken from differentperspectives, or projections, through the region of interest using atomosynthesis technique. The resulting three-dimensional model allows auser to inspect any plane through the region of interest, to review athree dimensional image to find defects such as voids. However, in orderto obtain a good result from tomosynthesis it is necessary to know withhigh accuracy the relative positions and orientations of the X-raysource, region of interest and detector. The way in which thetwo-dimensional images are combined in tomosynthesis relies on thisgeometric information, as it is required in the mathematical formulasthat are used. As a result, existing tomosynthesis systems require highprecision mechanical systems for moving the elements of the system i.e.X-ray source, region of interest and detector relative to one another.This need for high precision mechanical equipment makes tomosyntheticx-ray imaging systems much more expensive than two-dimensional x-rayimaging systems.

It would be desirable to provide a relatively inexpensive imaging systemthat is capable of providing a useful tomosynthetic model of a region ofinterest.

SUMMARY OF THE INVENTION

In a first aspect of the invention there is provided a method ofgenerating a three-dimensional representation of a region of interest ofa target object in for example, a tomosynthesis system. The methodcomprises the steps of:

-   -   a) identifying a fiducial marker of known geometry in a region        of interest of the target object or on a moveable surface which        is fixed relative to the region of interest;    -   b) creating a first image of the fiducial marker and first image        of the region of interest by detecting radiation from a        radiation source with a detector when the region of interest and        fiducial marker are in a first position relative to the        radiation source and the detector is in a first detector        position relative to the radiation source;    -   c) moving the fiducial marker and region of interest relative to        the radiation source to a second position relative to the        radiation source and moving the detector to a second detector        position relative to the radiation source;    -   d) creating a second image of the fiducial marker and a second        image of the region of interest by detecting radiation from the        radiation source with the detector when the region of interest        and fiducial marker are in the second position relative to the        radiation source and the detector is in the second detector        position relative to the radiation source;    -   e) generating corrected second image data for the region of        interest utilising a comparison of the second image of the        fiducial marker with information relating to an expected second        image of the fiducial marker; and    -   f) generating a three-dimensional representation of the region        of interest utilising the first image, or a corrected first        image data, and the corrected second image data for the region        of interest.

A method in accordance with the first aspect allows for the use ofrelatively inaccurate, and accordingly inexpensive, positioningmechanisms by correcting for positional inaccuracies during imageprocessing. Typically, the radiation source is stationary and the targetobject and detector are moved through predetermined positions relativeto the source. A method in accordance with the first aspect of theinvention uses a fiducial marker of known geometry on or near the regionof interest of a target object to adjust captured images of the regionof interest and fiducial marker to compensate for inaccuracies in thepositioning of the detector and the region of interest relative to theradiation source. In this method, both the region of interest andfiducial marker are moved through predetermined positions. The intendedspatial relationship between the radiation source, region of interest(and fiducial marker) and detector at each predetermined position isknown. The geometry of the fiducial marker is known (or is assumed to beknown). Using this information, together with a known or measuredinitial position of the fiducial marker, expected images of the fiducialmarker can be calculated for each predetermined position of the fiducialmarker and detector.

An image transform can then be calculated to map a captured image of thefiducial marker to the expected image of the fiducial marker at eachpredetermined position. This image transform can subsequently be used totransform captured images of the region of interest at eachpredetermined position in order to generate corresponding correctedimages of the region of interest for each predetermined position. Ineffect, the images are transformed to correspond to images that wouldhave been taken with the elements of the imaging system if they were inan ideal spatial relationship at each predetermined position.

These corrected images for each predetermined position are then combinedby tomosynthesis techniques to create a 3-D model, or image, of theregion of interest.

Thus, the method allows tomosynthesis techniques to be used withexisting x-ray imaging machines used for generating two-dimensionalimages, which do not otherwise have accurate enough mechanicalpositioning components to produce good quality three-dimensional images.In prior tomosynthesis systems, the position of the detector and targetobject need to be accurately known to within a fraction of a pixel onthe detector, typically within a fraction of a micron. This requires allof the mechanical components in the movement mechanisms to be highlyaccurately machined to within very tight tolerances. This is a majorfactor in the cost of tomosynthesis machines. Such tight tolerances arenot required with the present invention and accordingly, the methodprovides users with significant cost savings.

The method may comprise identifying a feature already present within theregion of interest as a fiducial marker. For example, a solder ball oran array of solder balls within the region of interest may be selectedas a fiducial marker. Each solder ball may be assumed to be rotationallysymmetric, and its size (and if an array of balls is used their spatialrelationship) determined within a first image. Using this information itis straightforward to calculate how the fiducial marker will appearwithin projections of the region of interest captured with the radiationsource, region of interest and detector in different predeterminedpositions. The fiducial marker may be selected by a user on screen usinga suitable user interface. The user interface may for example include amouse, a joystick, a keyboard or a touch sensitive screen which allow auser to draw a box, for example, around the fiducial marker with acursor.

Alternatively, or in addition, the method may comprise the step ofplacing a fiducial marker within the region of interest or close to theregion of interest on the target object or support for the targetobject. For example, a solder ball or other marker may be fixed onto acircuit board within a region of interest of the circuit board.Alternatively, if for example the region of interest is densely coveredwith components, a fiducial marker may be positioned outside the regionof interest but on the target object or support. The image capturemethod may then comprise capturing an image of the region of interestwhen the radiation source, region of interest and detector are in afirst position, i.e. have a first spatial relationship, and then movingthe support for the target object while keeping the detector stationaryso that the fiducial marker takes the place of the region of interest,so that the radiation source, fiducial marker and detector have thefirst spatial relationship. This process of capturing an image of one ofthe region of interest and the fiducial marker followed by the other ofthe region of interest and the fiducial marker is repeated for eachpredetermined position of the region of interest, fiducial marker andthe detector. The images of the fiducial marker and the region ofinterest can then be used in the same manner as in the case in which thefiducial marker is within the region of interest, to provide correctedimage data. This is possible without the introduction of significanterror because the movement of the detector and support for the targetobject, although not necessarily highly accurate, is typicallyrepeatable in a consistent manner, even when using inexpensive movementmechanisms for these components, such as servo motors.

It is also possible to use a fiducial marker provided for the purpose,already present on a target object but positioned outside the region ofinterest, or even for the support to include a fixed fiducial marker ormarkers. For example, it may be desirable for a manufacturer of circuitboards to include a fiducial marker in a predetermined position on eachcircuit board during manufacture. The fiducial marker may advantageouslybe placed in a relatively empty portion of the circuit board. In thiscase, if the fiducial marker is outside the region of interest, themethod comprises capturing an image of one of the region of interest andthe fiducial marker followed by the other of the region of interest andthe fiducial marker for each predetermined position of the region ofinterest, fiducial marker and the detector.

The method may further comprise the steps of creating corrected imagedata for subsequent predetermined positions of the region of interest,fiducial marker and detector, such as creating a third image of thefiducial marker and a third image of the region of interest by detectingradiation from the radiation source with the detector when the region ofinterest and fiducial marker are in a third position relative to theradiation source and the detector is in a third detector positionrelative to the radiation source; and generating corrected third imagedata for the region of interest utilising a comparison of the thirdimage of the fiducial marker with information relating to an expectedthird image of the fiducial marker, wherein the step of generating athree-dimensional representation of the region of interest utilises thecorrected third image data.

The method may advantageously comprise generating images of the regionof interest and fiducial marker from many different positions andgenerating corresponding corrected image data for the region of interestfor each position. The greater the number of predetermined positions forthe region of interest, fiducial marker and detector, the moreinformation can be included in the three-dimensional representation ofthe region of interest.

The fiducial marker may comprise a plurality of fiducial markerelements. For example, the fiducial marker may comprise two, three ormore solder balls. The fiducial marker elements may be spaced throughoutthe region of interest. Arrays of fiducial markers that are arranged togive information throughout the image, or from an area of the image thatshows errors typical of the whole image, can provide information for thecorrection of rotation, scale, keystone distortions or higher ordertransforms. A single fiducial marker positioned inside the area ofinterest could be unavoidably obscured by other components inside thearea of interest. That could cause imprecision in fiducial detection andsubsequently in image transformation. However, having an array offiducial markers increases precision and makes detection much morerobust. It is highly unlikely that all fiducials will be obscured byother components at the same time. Having at least one fiducial withoutocclusion at time is sufficient for accurate detection.

The fiducial marker may have a predetermined non-symmetric shape. Forexample, the fiducial marker may take the form of a star with one armmissing. Non-symmetric shapes may provide more information aboutrotational errors by providing an absolute index of position, as well asabout distortions due to pitch or tilt of the support or detector, thanhighly symmetric fiducial markers. Such distinctive shapes may also havethe advantage of being unambiguously recognisable in each image.

However, for simple processing, a spherical shaped marker may be used,such as a solder ball. The expected second image of the fiducial markermay then be calculated based on an assumption that the fiducial marker,or each fiducial marker element, has rotational symmetry. Thissimplifies the required image processing.

In a second aspect of the invention, there is provided a system forgenerating a three-dimensional representation of a region of interest ona target object comprising:

-   -   an x-ray source;    -   a support configured to support the region of interest and a        fiducial marker of known geometry and a support transport        mechanism configured to move the support;    -   an x-ray detector and detector transport mechanism configured to        move the detector;    -   a motion controller connected to the support transport mechanism        and the detector transport mechanism, the motion controller        configured to supply command signals to the support transport        mechanism to move the region of interest and fiducial marker        from a first position to a second position and to supply command        signals to the detector transport mechanism to move the detector        from a first detector position to a second detector position,        such that x-rays from the x-ray source are transmitted through        the region of interest and the fiducial marker to the detector        when the region of interest and fiducial marker are in the first        position and the detector is in the first detector position, and        when the region of interest and fiducial marker are in the        second position and the detector is in the second detector        position;    -   an image processor coupled to the detector configured to receive        signals from the detector to generate images of the region of        interest and fiducial marker, wherein the image processor is        configured to:    -   calculate an expected image of the fiducial marker in the second        position,    -   generate corrected image data for the region of interest in the        second position using a comparison of the expected image of the        fiducial marker in the second position with the image of the        fiducial marker in the second position; and    -   generate a three-dimensional representation of the region of        interest utilising an image of the region of interest in the        first position or corrected image data for the region of        interest in the first position, and the corrected image data for        the region of interest in the second position.

The system may further comprise a visual display configured to displayimage data based on signals from the detector, and a user interface,wherein the user interface is configured to allow a user to select afiducial marker from within an image on the display.

The detector transport mechanism may comprise a pivotable, arcuate trackto which the detector is coupled. The support transport mechanism may beconfigured to allow the support to move independently in threeorthogonal directions. The image processor may be configured to carryout any of the method steps of the first aspect of the invention.

In a third aspect of the invention, there is provided a computerreadable storage medium and which enables the user to practice themethods of this invention with an x-ray imaging apparatus. The x-rayimaging apparatus comprises: an x-ray source; a support transportmechanism that moves a support for a region of interest and a fiducialmarker of known geometry; an x-ray detector; a detector transportmechanism configured to move the detector; and a motion controllerconnected to the support transport mechanism and the detector transportmechanism, the motion controller configured to supply command signals tothe support transport mechanism to move the region of interest andfiducial marker from a first position to a second position and to supplycommand signals to the detector transport mechanism to move the detectorfrom a first detector position to a second detector position such thatx-rays from the x-ray source are transmitted through the region ofinterest and the fiducial marker to the detector when the region ofinterest and fiducial marker are in the first position and the detectoris in the first detector position, and when the region of interest andfiducial marker are in the second position and the detector is in thesecond detector position. Given this apparatus, the computer readablestorage medium stores executable instructions that, when executed by acomputer processor connected to the apparatus, cause the computerprocessor to:

-   -   request a user to select a region of interest and select a        fiducial marker;    -   generate images of the region of interest and the fiducial        marker in the first and second positions based on received image        data,    -   generate an expected image of the fiducial marker in the second        position,    -   generate corrected image data for the region of interest in the        second position using a comparison of the expected image of the        fiducial marker in the second position with the image of the        fiducial marker in the second position;    -   generate a three-dimensional representation of the region of        interest utilising an image of the region of interest in the        first position, or corrected image data for the region of        interest in the first position, and the corrected image data for        the region of interest in the second position.

The computer readable storage medium may also hold executableinstructions that, when executed by a computer processor connected tothe x-ray imaging apparatus, control operation of the motion controller.The computer readable storage medium may also hold executableinstructions that, when executed by a computer processor connected tothe x-ray imaging apparatus, carry out any of the method steps of thefirst aspect of the invention.

In a fourth aspect, the invention provides a computer readable storagemedium in accordance with the third aspect, in combination with one ormore fiducial markers that can be secured in a fixed position relativeto the region of the of interest in such a way that the fiducial markersmaintain a fixed position relative to the region of interest when theyare moved with the region of interest.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described in detail, by way ofexample only, with reference to the accompanying drawings, in which:

FIG. 1 is a schematic drawing showing components on an x-ray imagingsystem;

FIGS. 2A-2C are isometric views of a support stage, x-ray source anddetector in accordance with an embodiment of the present invention;

FIG. 3 is a schematic drawing showing the elements of an imaging systemin accordance with an embodiment of the invention;

FIG. 4 illustrates the field of view of a detector and a fiducialmarker;

FIG. 5 illustrates some exemplary fiducial markers;

FIG. 6 is a flow diagram illustrating a method in accordance with oneembodiment of the invention; and

FIG. 7 is a flow diagram illustrating a modification to the method shownin FIG. 6 in accordance with another embodiment of the invention.

DETAILED DESCRIPTION

FIG. 1 is a schematic illustration of the basic elements of an x-rayimaging system. The system shown in FIG. 1 comprises an x-ray source 10,which in this system is held stationary, a moveable support 12 and amoveable detector 14. It is advantageous to keep the x-ray sourcestationary as it is a relatively bulky and massive component. It alsorequires very large power cables which are relatively inflexible anddifficult to move. X-rays from the x-ray source 10 pass through thesupport and any target objects mounted on the support, and impinge onthe detector 14. FIG. 1 illustrates the areas 16 on the supportcorresponding to the field of view of the detector 14. The field of viewof the detector is selected by a user by the relative positioning of thedetector 14, support 12 and x-ray source 10 so that the region ofinterest of the target object is within the field of view of thedetector. The detector can move to different positions so that differentprojections can be taken through objects on the support. In thiscontext, a different projection means that the x-rays pass through theobject on the support in a different direction. The detector 14 istypically moved to successive positions within an XY plane above thesupport 12 to collect a series of different projections at the samemagnification. An exemplary mechanism for moving the detector isillustrated in FIG. 2, but any suitable mechanism may be used.

The support 12 is moveable in the XY plane in order that regions ofinterest on the support can be moved to a position between the x-raysource and the detector. In the example shown in FIG. 1, the support 12is also moveable in a vertical or Z direction. This allows themagnification of the detected image at the detector to be adjusted, i.e.larger or smaller areas of the support can be made to fall within thefield of view of the detector depending on the relative distance betweenthe x-ray source and the support and the x-ray source and the detector.As explained, the region of interest must fall within the field of view.It is preferable that the field of view is a little larger that theregion of interest as the quality of the three-dimensional modelproduced is poorer at the edges of the field of view. This is becausethe images do not all overlap each other perfectly so the edges of thethree dimensional model are generated from fewer images than the centralarea. However, to provide for the best resolution, the user shouldselect the smallest field of view that allows for a good quality threedimensional model of the entire region of interest.

In FIG. 1, the detector 14 is shown in four different positions andthere are four corresponding regions 16 on the support. It should beunderstood that many more positions are possible. A three dimensionalmodel may be constructed from any number of projections, and anythingbetween 12 and 720 projections is used in practice.

Generally, the x-ray source 10 includes a tube that generates the beamof x-rays by accelerating electrons from an electron gun and causing theenergetic electrons to collide with a metal target. In one embodiment,the x-ray source may be a stationary or non-steerable type of source,which lacks the capability to move the electron beam to strike the metaltarget at more than one location. The x-rays contained in the beam aresufficiently energetic to penetrate through the thickness of targetobjects on the support 12 so that attenuated x-rays reach the detector14. The differential levels of x-ray attenuation by the materials ofdifferent density within the region of interest produces contrast in theresulting image captured by the detector.

A typical target object which can be mounted on the support 12 is aprinted circuit board containing electronic components, integratedcircuits and bonds between components and circuit elements. There may bea plurality of circuit boards mounted on the substrate at any one time,but with a single movable detector, only a single region of interest isimaged within the field of view of the detector at any one time.

The detector 14 shown in FIG. 1 may be a digital detector and have aconstruction as is well known in the art. Generally, the detectorincludes an active area, a sensor that converts the incoming x-rays overthe active area into another signal type that can be measured or imaged,and an amplifier used to boost the amplitude of the signals. The signalsare converted from an analogue form to a digital form within thedetector 14 and a digital image formatted output from the detector. Anexemplary digital detector is a digital charged coupled device (CCD)camera, such as a complementary metal oxide semiconductor (CMOS) flatpanel detector that includes a two dimensional pixel array of siliconphoto diodes constituting the active area. In one embodiment, thedetector is a flat panel detector characterised by a 3 megapixel 150mm×120 mm active area. The active area of the detector 14 faces towardsa region of interest on the support and the x-ray source so that thex-rays passing through the region of interest impinge on the detectorwhen the region of interest and detector are properly positioned.

FIGS. 2A-2C illustrate an example of an x-ray apparatus that can be usedwith this invention having a support stage, x-ray source and detector.The apparatus includes a frame 20 that is supported on feet 21, whichthemselves are mounted within a cabinet (not shown). This cabinet is ofthe usual kind and provides a shielded enclosure to protect users fromthe harmful effects of x-rays. Mounted on the frame 20 is the x-ray tube10 for generating x-rays, and the x-ray detector 14. Between the x-raysource and the detector is the moveable support 12, later described indetail, adapted to support a target object having a region of interestto be imaged.

Each pair of feet 21 supports a respective beam 25 of the frame 20. Notethat in FIGS. 2B and 2C, the legs 21 and beams 25 are removed to moreclearly show other components. Cross beams 90 rest upon beams 25. Thebeams 25 and cross beams 90 comprise a generally rectangular perimeterframe. The frame 20 also includes a main support plate 26 that isattached to the beams 90 in a substantially vertical plane. The supportplate 26 is relatively massive and rigid and comprises the principlestructural element of the frame 20.

The x-ray tube 10 is directly mounted to one side of the support plate26. The tube 10 is located centrally with respect of the feet 21 andthus the plate 26 is slightly offset to one side. On the other side ofthe support plate 26 is directly mounted the z axis motor 43 which canvertically position the moveable support 12 on which a target objectcontaining the region of interest is secured.

As best shown in FIG. 2B, movable support 12 is comprised of a Y table12 a mounted on top of an X table 12 b. Y axis motor 42 moves Y table 12a in the Y direction and X axis motor 41 moves both Y table 12 a and Xtable 12 b in the X direction. Z axis motor 43 reciprocates shaft 76vertically. Shaft 76 is connected to X table 12 b to move X table 12 band Y table 12 a vertically.

The lateral ends of the support plate 26 have rigid cheeks 96 on whichare directly mounted bearings 30 of an arcuate frame 31. The ends of theframe comprise counterweights 32. The inner side of the frame comprisesa track 33 that follows the circumference of a circle centred on thex-ray source 10.

Mounted on the track 33 is the x-ray detector 14. As best shown in FIG.2C, a motor 44, via shaft 82, causes the arcuate frame 31 to pivot andmotor 45 moves the detector along track 33. In one embodiment, thedetector 14 can be moved around the x-ray source from a verticalposition, generally in the range of plus or minus 60 degrees to eitherside of vertical.

In use, the target object containing the region of interest, as welloptionally of one or more fiducial markers, is secured to the uppersurface 78 of Y table 12 a. The cabinet is closed, and the x-ray tube isenergised to stimulate the production of x-rays. These x-rays radiate instraight lines from the spot source, and the detector and support aremoved until the sample is imaged in the desired orientation. The imagemay for example be displayed on an external screen of the cabinet,provided adjacent to suitable controls such as a mouse and keyboard orone or more joysticks. The relative position to the sample and/ordetector may be moved to image the sample from the desired direction andat the appropriate magnification.

Some current computed tomography products provide a horizontal rotaryaxis on which the sample is rotated. This complete rotation provides agood data set due to the complete rotation of the object but limits thesize of the sample that can be used with this type of equipment. Thepresent invention uses existing machine geometry but provides a conicalpath of movement for the sample and detector. This allows larger objectsto be reconstructed without cutting them down, but does not provide ascomplete a data set as systems which provide for complete rotation ofthe sample.

FIG. 3 is a schematic illustration of the electronic and controlelements of a system in accordance with the present invention. Themechanical components of the system are as described with reference toFIGS. 2A-C. The system comprises a motion controller or servo system 40that is operable to control the movement of both the support for atarget object to be imaged and to control corresponding movement of thedetector. As previously described, the system includes a motor 41 formoving the support surface in an X direction, a motor 42 for moving thesupport surface in a Y direction and a motor 43 for moving the supportsurface in a Z direction. The movement of the detector is achieved by amotor 44 operable to pivot the arcuate frame on which the detector ismounted, and a motor 45 configured to move the detector along the trackon the arcuate frame.

The motion controller 40 is connected to a processor 48 which may be adedicated microprocessor or may be a suitably programmed general purposecomputer, such as a PC. The processor 48 sends instructions to themotion controller 40, which then sends control signals to the motors41-45, as will be described in more detail.

The processor 48 is also configured to control activation anddeactivation of the x-ray source 46.

The processor 48 receives output signals from the x-ray detector 47 andsends corresponding images to a display 50. An interface 51 is providedto allow a user to activate an image capture process as well as toconfigure parameters in the operation of the processor and to selectportions of a sample as regions of interest. The detector supplies imagedata to the processor continuously during operation, so that the fieldof view of the detector can be displayed continuously on the display 51.

The processor 48 may include a memory 49 as shown in FIG. 3.Alternatively, or in addition, a memory may be provided in an externaldevice connected to the processor. FIG. 3 illustrates in dotted outlinean external computer 52 that may be connected to the processor 48 andmay be configured to provide memory as well as image processingfunctions. There may be advantages to having image processing functionscarried out on a separate processor to image capture functions, so thatimage processing for one region of interest can be carried out at thesame time as image capture is carried out on the next region ofinterest.

The processor 48 is configured to control and coordinate the operationof the x-ray source 10, support 12 and detector 14 to capture aplurality of projections of a single region of interest, as is describedin more detail with reference to FIGS. 6 and 7. By taking multipleprojections of a particular region of interest with different region ofinterest and detector positions, a collection of projections for thatregion of interest can be made. The collection can then be processedusing a tomosynthesis algorithm to produce a three dimensional model ofthe region of interest. Various tomosynthesis algorithms and processingtechniques are known in the art, such as the ReconPro reconstructionsolution offered by Prexion Inc. of 411 Borel Avenue, Suite 550, SanMateo, Calif. 94402, USA.

A requirement for generating a three dimensional model using a pluralityof images is a knowledge of the precise spatial relationship betweenx-ray source, region of interest and detector for each image. Inpractice, in order to get useful results this has meant the use ofexpensive machinery. The high expense is caused, in particular, by thevery tight tolerances required for all of the components of the movementmechanisms for the region of interest and detector.

In the present invention, this problem is overcome by using a fiducialmarker or markers. Image processing techniques are then used to altercaptured images to correspond to how those images would look were thecomponents accurately positioned. Instead of accurate control of themoving parts of the system, corrections are applied to captured imagesto provide a set of corrected images and the corrected images are thencombined using a tomosynthesis algorithm to generate a three dimensionalmodel.

The fiducial marker may take the form of an element already existing ona target object or may be an element fixed to the target object, orfixed close to the target object on the support on which the targetobject is mounted, prior to the imaging process.

FIG. 4 shows an exemplary region of interest on circuit board. Thisparticular region of interest includes an integrated circuit component60 as well as a ball grid array 61 comprising a plurality of solderballs used for bonding components to the underlying integrated circuitboard. Another region of interest could be much smaller, comprising oneor two solder balls for example. The solder balls 61 can be used aseffective fiducial markers as they can be assumed to have a sphericalgeometry. One, two or more solder balls may be used as a fiducialmarker. In practice, using several solder balls is beneficial as thesolder balls are not absolutely spherical. Using multiple solder ballsas fiducial markers reduces any error associated with their imperfectsymmetry. Other existing components on target objects can be used ifthey have a known geometry and that geometry can be accommodated withinthe image processing process carried out by the system. Vias within thePCB or semiconductor package have very similar properties to solderballs. In addition, the more complex but predictable geometries ofcomponents such as Quad-Flat No-Lead packages can be utilised.

Alternatively, fiducial markers designed for the purpose may be used.These fiducial markers may be fixed to the target object or to thesupport close to the target object. FIGS. 5 a to 5 e illustrate someexemplary fiducial marker shapes. The fiducial marker may be formed fromany suitable material opaque to x-rays at the typical energy levelsused. The scale of the fiducial marker used needs to be appropriate forthe field of view and object under inspection and so a variety ofdifferent size fiducial markers may be provided together with the x-rayequipment or software package.

The fiducial markers in FIGS. 5 a, 5 b and 5 c are generally flatmarkers, but they do have some height to them. They are formed so as tohave similar x-ray absorption to the components of the region ofinterest and so may have similar density, material properties andthickness to components in the region of interest. Advantageously theyare made with as low a height as possible in order to minimise obscuringof the region of interest.

The fiducial markers in FIGS. 5 d and 5 e are spherical markers(although they could equally be discs). Suitable spherical markers, ofbetween 100 μm and 0.8 mm in diameter, can be obtained from suppliersfor bearings used in instrumentation. These bearing are more perfectlyspherical that solder balls and so make better fiducial markers.

As will be described, the fiducial marker or markers may be within theimaged region of interest or may be outside the imaged region ofinterest. Whichever arrangement is used, the fiducial markers must berecognisable within each projection. This recognition is doneautomatically using image recognition techniques incorporated into thesoftware running on the processor. The expected image of the fiducialmaker or markers may be compared to the captured images of the fiducialmaker or markers within the imaged region using a correlation approachsuch as provided by the VisionPro software product of, CognexCorporation, 1 Vision Drive, Natick, Mass. 01760-2059, United States.This software calculates a transform between the expected and capturedimages of the fiducial marker at a predetermined position of thefiducial marker between the source and detector. That transform can thenbe applied to the captured image of the region of interest at thatpredetermined position to generate a corrected image of the region ofinterest for that predetermined position.

Having described the components of the system illustrated in FIGS. 2A-Cand 3, and illustrated some examples of fiducial markers in FIG. 5,exemplary methods of operation will be described with reference to FIGS.6 and 7.

FIG. 6 illustrates the steps of an imaging method in which the fiducialmarker is within the region of interest. After the process is started instep 600, the user can select, in step 605, various operatingparameters, such x-ray tube accelerating voltage and power, the numberof projections (i.e. images) to be taken, the angular range from thevertical that the detector 14 (and support 12) travels across as theimages are taken, and the magnification. As can be seen in FIG. 2A-2C,the detector can move around a hemisphere and, in principle, projectionsmay be taken with the detector in any position on that hemisphere. Thegreater the angle from the vertical that the detector is at, the moreinformation can be recovered about the region of interest. However, inpractice it is desirable to limit the angle from the vertical to whichthe detector travels. This is because at large angles the x-rays willtravel through more extraneous components before (and potentially after)reaching the region of interest. So the user has to find a balance byusing the maximum angle before the noise in the projections produced byextraneous objects outweighs the benefit of the large angle. This willdepend in large part on the topography of the target object. In order tosimplify image processing, the detector in the described embodiments isconstrained to move to positions on a circle in an x-y plane above theregion of interest, so that all projections are taken at the same angleto the vertical.

The user also selects the number of projections to be taken, and thechoice may be a balance between time constraints and the required detailin the final three dimensional model. Any number may be used, althoughit is typically between 12 and 720 projections.

For example, if the user selects 72 projections to be taken, selects anangle of 30° from the vertical, and a particular magnification, theprocessor calculates 72 different relative positions for the x-raysource 10, support 12 and detector 14 according to those parameters. Theresult will be the initial position of the support 12 and detector 14and 71 different positions to which the support 12 and detector 14 wouldbe moved equally spaced around a circular path, defining a cone angle of30° with respect to the x-ray source. The 71 positions would be thepredetermined positions through which the support 12 and detector 14would be moved. It should be clear that some or all of these parametersmay be selected or adjusted later in the process, at any time before thefirst image is recorded.

In step 610, a decision must be made whether to use elements alreadypresent within the region of interest as a fiducial marker or whether tofix a fiducial marker on to the target object within the region ofinterest. If elements already present on the target object are to beused as a fiducial marker, the process continues in step 620. If anexternally supplied fiducial marker is required, this marker is fixed tothe target object in step 615. Any suitable fixing technique can beused, sufficient to keep the fiducial marker fixed in position relativeto the region of interest during the imaging process.

In step 620, the user must select the field of view of the detector. Asexplained, the field of view must include the region of interest of thetarget object. The field of view is preferably larger than the region ofinterest, as the quality of the three dimensional model produced isgreatest in the centre of the field of view and relatively poor at thecorners and edges where part of the object of interest may not be seenin all the projections, but no larger than necessary for a good qualitythree dimensional model of the region of interest. The field of view maybe selected on screen using the user interface such as by using thecursor to draw a box around the field of view. Selection of the field ofview is typically done with the detector and region of interestdirectly, or vertically, above the x-ray source. Once the field of viewhas been selected, inputs from a user through the user interface 51cause the processor 48 to send command signals to the motion controller40. In response, the motion controller 40 adjusts the position of thedetector 14 and support 12 in accordance with the command signals todisplay the selected field of view. The user can continue to adjust thepositions of the detector 14 and support 12 until the field of view isas desired.

Having selected the field of view, the fiducial marker or markers mustbe identified in step 625. In this embodiment the fiducial marker iswithin the region of interest and so within the selected field of view.To select the fiducial marker, the detector and support are now movedfrom a position directly, or vertically, above the x-ray source to aninitial position which places them at the desired angle from verticalfor the first projection. The fiducial marker is selected on screenusing the user interface. The user may identify the fiducial markerusing a cursor or dragging a box or boxes around a portion or portionsof the field of view on the display screen. With the support 12 anddetector 14 in their initial positions, a first image of the field ofview containing the region of interest is then recorded by the detectorin step 630 and stored in memory 49. The portion or portions of theimage selected as fiducial markers by the user are also stored in memory49. The image and position of the fiducial marker or markers is used asthe basis for calculating expected images of the fiducial marker ormarkers in each of the subsequent projections recorded by the detector.The system knows the geometry and position of the fiducial markers andknows the predetermined positions of the support and detector at whicheach projection. Using this information it is possible to calculate anexpected image and position of the fiducial markers at the projectiontaken at each predetermined position.

The support 12 and detector 14 must then be moved through each of thepredetermined positions in order to record an image of the region ofinterest and fiducial marker at each position. As previously described,the position of the support 12 and detector 14 for each projection iscalculated by the processor 48 based on the parameters set by the user.In the example previously described, the user selected 72 projections tobe taken, an angle of 30° from the vertically above the X-ray source forthe detector and a particular magnification, and in turn, the processorcalculated 72 different relative positions for the x-ray source 10,support 12 and detector 14 according to those parameters. In steps 635,640 and 645 the motion controller moves the support 12 and detector 14sequentially to each of the remaining 71 predetermined positions and thedetector 14 records an image of the field of view containing the regionof interest and fiducial marker in each position. The motion controllersends incremental signals to servo motors 41-45 in order to move thesupport and detector to the next position in the sequence. The steps 640and 645 are repeated until all of the required images have been recorded(FIG. 6 illustrates steps 640 and 645 being repeated n times). After allthe required images have been recorded, a signal is sent from step 640to step 660 to generate the 3D model of the region of interest from thecorrected images of the region of interest.

The calculation of the expected images of the fiducial marker is shownas step 650. As already described, the desired spatial relationshipbetween x-ray source, region of interest and detector for eachprojection is calculated based on the parameters set by the user. So,based on the spatial relationship and knowledge of the geometry andposition of the fiducial marker, expected images and positions of thefiducial marker can be calculated for each position. In this example,the fiducial marker is assumed to have a rotational symmetry about thevertical axis and the detector constrained to move around a circularpath of fixed cone angle with respect to the x-ray source, so that thefiducial marker appears the same size and shape in each projection, withonly its position within the field of view changing. However, thefiducial marker may have a more complex geometry if desired. Adescription of that geometry is then included as a parameter in theimage processing calculations carried out by the processor.

The calculation of expected images of the fiducial marker in step 650can be carried out simultaneously or sequentially with the image capturesteps 635 to 645. Step 650 may also be carried out on a separateprocessor 52 to the image capture processing, as described withreference to FIG. 3.

In step 655, for each predetermined position, each of the expectedimages of the fiducial marker or markers is compared to thecorresponding captured image of the fiducial marker. For eachpredetermined position, the processor 48 (or 52) calculates a transformto map the captured image of the fiducial marker or markers onto theexpected image. This is done by identifying specific features of thefiducial markers or positions of fiducial markers by correlation or edgeextraction from the image and finding their spatial relationship. Thistransform for each predetermined position is then applied to thecaptured image of the region of interest at that predetermined positionto generate a corrected image for the region of interest at thatpredetermined position. The corrected image is effectively the imagethat would have been captured had the positioning mechanism been able toaccurately position the support and detector as desired.

Once images of the region of interest for all the predeterminedpositions have been corrected, the corrected images are combined in step660, in response to the signal from step 640, to generate a threedimensional model of the region of interest. These images can becombined using a tomosynthesis algorithm, such as the ReconProreconstruction solution offered by Prexion Inc., referenced above.

The three dimensional model is then made available for viewing by theuser on the display 50 and different slices through the model may beselected for viewing by the user using the user interface 51 in order tolook for defects such as the level of voiding within a joint andincomplete solder joints. This defect analysis is useful both foroptimising manufacturing processes and for process control by checkingthat manufactured items are remaining consistent and meeting qualitythresholds.

FIG. 7 illustrates a modification of the method shown in FIG. 6, whichallows the use of a fiducial marker outside of the region of interest.If, for example, the region of interest is densely covered withelectronic components, a fiducial marker may be positioned outside theregion of interest but on the same substrate or directly on the support.The method in the embodiment of FIG. 7 includes the same initial steps600 to 620 shown in FIG. 6. FIG. 7 shows only the subsequent steps inthe method. In step 700 the fiducial marker must be identified by theuser. This requires changing the field of view of the detector from thefield of view selected for the region of interest in step 620 to a fieldof view encompassing the fiducial marker. To do this, using the userinterface 51 and screen 50, the user controls the movement of thesupport 12 (ideally within the same XY plane so the magnification isunchanged), while the detector 14 remains stationary. The support ismoved to a position such that the desired fiducial marker is within thefield of view and ideally in the centre of the screen. The detector andsupport are then moved from a position directly, or vertically, abovethe x-ray source to an initial position which places them at the desiredangle from vertical for the first projection, just like is describedabove in the case where the fiducial is within the field of view of theregion of interest. The fiducial is then identified using a cursor or bydragging a box around the image of the fiducial on the screen.

During the above process, the x and y position of the field of view forthe fiducial relative to the x and y position of the field of view forthe region of interest are stored. These x and y positions, which can bestored in memory as x and y offset signals, are then used later to movethe support between the position of the field of view for the region ofinterest and the position of the field of view for the fiducial marker,under control of the x and y motors 41, 42.

The image capture process then proceeds by recording an image of thefield of view containing the region of interest followed by an image ofthe field of view containing the fiducial marker for each predeterminedposition of the detector and region of interest. In step 705 an image ofthe region of interest is recorded for the first predetermined position.The support is then moved in step 710 using the stored x and y offsetsignals, while the detector is held stationary relative to the x-raysource, so that the fiducial is in the first predetermined position. Afirst image of the field of view containing the fiducial is thenrecorded in step 715. It should be appreciated that step 700 may becarried out after step 710 instead of beforehand, and in practice thismay be more convenient for the user. It should also be appreciated thatthe fiducial marker may be imaged before the region of interest insteadof after it for each predetermined position of the region of interestand detector.

In step 720 both the detector and the support (i.e. the region ofinterest) are moved to the next predetermined position corresponding tothe next projection of the region of interest. In step 725, an image ofthe field of view containing the region of interest is recorded at thisnext predetermined position. In step 730, the support is moved using theXY offset signals, while the detector is held stationary relative to thex-ray source, until the fiducial has been positioned at thepredetermined position at which the image of the region of interest wasjust recorded. In step 735 an image of the field of view containing thefiducial marker at this predetermined position is recorded. The processthen returns to step 720 and steps 720 to 735 are repeated until imagesof the region of interest and of the fiducial marker are captured foreach predetermined position of the region of interest and detector. Asdescribed below, after images have been captured for all predeterminedpositions, a signal is sent from step 722 step 752 generate the threedimensional model.

In step 740, the calculation of expected images of the fiducial markeris carried out in the same manner as described with reference to FIG. 6.In step 745, for each predetermined position, each of the expectedimages of the fiducial marker is compared to the corresponding capturedimage of the fiducial marker and a transform is calculated for eachcaptured image to map it onto the expected image. The same technique maybe used as described with reference to FIG. 6. The transform for eachpredetermined position is then applied to the corresponding capturedimages of the region of interest to generate corrected images of theregion of interest for each predetermined position. A corrected image ofthe region of interest is generated for each projection following thefirst image. As previously mentioned, when a signal is received at step750 from step 720 that images for all predetermined positions have beencaptured, the first image and subsequent corrected images are thencombined in a tomosynthesis algorithm in step 750 to generate a threedimensional model of the region of interest.

Separate imaging of the region of interest and the fiducial marker ispractical with relatively inaccurate positioning mechanisms, providedthe movement of the support is repeatable. So while it may not bepossible to accurately move the support for each movement of thefiducial marker to the predetermined positions of the region ofinterest, the control signal is the same and the resulting movement isthe same. With regard to step 730, it should be appreciated that it maybe the detector rather than the support that is moved between the regionof interest and the fiducial marker while the support remainsstationary. In the mechanism shown in FIG. 2 it is preferable to keepthe detector stationary and move the support as the movement of thesupport is more repeatable. However that may not be the case withdifferent mechanical arrangements.

The invention has been described with reference to particularembodiments, but it should be clear that many modifications may be madeto the system and method while using the same inventive concept. Forexample, different systems may be used for moving the target object andthe detector, that introduce different errors in the resulting capturedimages. Regardless of the system used, the use of suitable fiducialmarkers allows corrected images to be generated.

1. A method of generating a three-dimensional representation of a regionof interest on a target object, comprising the steps of: identifying asingle fiducial marker having one or more marker elements ofpredetermined known geometry in a region of interest of the targetobject or on a moveable surface which is fixed relative to the region ofinterest; creating a first image of the single fiducial marker and firstimage of the region of interest by detecting radiation from a radiationsource with a detector when the region of interest and single fiducialmarker are in a first position relative to the radiation source and thedetector is in a first detector position relative to the radiationsource; performing the following steps for each of a plurality ofdesired second positions of the region of interest and single fiducialmarker and corresponding desired second detector positions: moving thesingle fiducial marker and region of interest relative to the radiationsource to a second position relative to the radiation source and movingthe detector to a second detector position relative to the radiationsource; creating a second image of the single fiducial marker and asecond image of the region of interest by detecting radiation from theradiation source with the detector when the region of interest andsingle fiducial marker are in the second position relative to theradiation source and the detector is in the second detector positionrelative to the radiation source; determining an expected second imageof the single fiducial marker for a corresponding desired secondposition of the region of interest and single fiducial marker anddesired second detector position based on the predetermined knowngeometry of the single fiducial marker; generating corrected secondimage data for the region of interest by utilizing a comparison of thesecond image of the single fiducial marker with information relating tothe expected second image of the single fiducial marker at thecorresponding desired second position to determine an image transformthat maps the second image of the single fiducial marker to the expectedsecond image of the single fiducial marker, and applying the imagetransform to the second image of the region of interest to generate thecorrected second image data for the region of interest, the correctedsecond image data thereby being the image that would have been capturedif the second image of the single fiducial marker and of the region ofinterest were created at the desired second position and desired seconddetector position; and generating a three-dimensional representation ofthe region of interest utilizing the first image of the single fiducialmarker and of the region of interest, and the corrected second imagedata for each of the desired second positions.
 2. The method accordingto claim 1, wherein the method comprises placing the single fiducialmarker on the region of interest or on the moveable surface.
 3. Themethod according to claim 1, wherein the single fiducial marker iswithin each image of the region of interest.
 4. The method according toclaim 1, wherein each image of the single fiducial marker is separatefrom each image of the region of interest, and wherein the step ofcreating a first image of the single fiducial marker and a first imageof the region of interest comprises holding the detector in a firstdetector position while moving the region of interest and singlefiducial marker sequentially to the first position.
 5. The methodaccording to claim 4, wherein the step of creating the second image ofthe single fiducial marker and the second image of the region ofinterest is carried out after the step of creating the first image ofthe single fiducial marker and creating the first image the region ofinterest.
 6. The method according to claim 1, wherein a plurality offiducial marker elements are identified in the region of interest, whicheach have a predetermined known geometry and are fixed relative to theregion of interest, and the additional fiducial marker elements beyondthe single fiducial marker are used during correction of the secondimage data correct for error that is associated with imperfect geometryof the single fiducial marker.
 7. The method according to claim 1,wherein the expected second image of the single fiducial marker iscalculated based on an assumption that the single fiducial marker hasrotational symmetry.
 8. A system for generating a three-dimensionalrepresentation of a region of interest on a target object using a numberof projections, the system comprising: an x-ray source; a supportconfigured to support the target object and a single fiducial markerhaving one or more marker elements of predetermined known geometry and asupport transport mechanism configured to move the support, thepredetermined known geometry of the single fiducial marker defining aninput parameter; an x-ray detector and detector transport mechanismconfigured to move the detector; a motion controller connected to thesupport transport mechanism and the detector transport mechanism, themotion controller configured to supply command signals to the supporttransport mechanism to move the region of interest and the singlefiducial marker from a first position to a plurality of second positionscorresponding to the number of projections and to supply command signalsto the detector transport mechanism to move the detector from a firstdetector position to a plurality of second detector positionscorresponding to the number of projections, wherein the plurality ofsecond positions and the plurality of second detector positions areintended to correspond to a plurality of desired second positions anddesired second detector positions relative to the x-ray source, whichare based on desired movement of the region of interest and the detectoraround the x-ray source to capture the number of projections, such thatx-rays from the x-ray source are transmitted through the region ofinterest and the single fiducial marker to the detector when the regionof interest and single fiducial marker are in the first position and thedetector is in the first detector position to cause the detector togenerate first position image information, and transmitted again whenthe region of interest and single fiducial marker are in one of theplurality of second positions and the detector is in one of theplurality of second detector positions to cause the detector to generatesecond position image information; an image processor coupled to thedetector and configured to receive the first position image informationand the second position image information from the detector to generatea first image of the region of interest and a first image of the singlefiducial marker using the first position image information, and togenerate a second image of the region of interest and a second image ofthe single fiducial marker using the second position image information,wherein the image processor is configured to: determine an expectedsecond image of the single fiducial marker in each of the plurality ofdesired second positions based on the input parameter of thepredetermined known geometry of the single fiducial marker, generate acorrected second image of the region of interest for each of theplurality of desired second positions using a comparison of the expectedsecond image of the single fiducial marker in the desired secondposition with the second image of the single fiducial marker that isgenerated at the corresponding second position, to determine an imagetransform that maps the second image of the single fiducial marker tothe expected second image of the single fiducial marker, and then applythe image transform to the second image for the region of interest, thecorrected second image data thereby being the image that would have beengenerated if the second image of the single fiducial marker and of theregion of interest were actually generated at the desired secondposition and desired second detector position; and generate athree-dimensional representation of the region of interest utilizing thenumber of projections of the region of interest, the number ofprojections being more than two, and which include the first image ofthe single fiducial marker and of the region of interest, and thecorrected second image data for each of the desired second positions. 9.The system according to claim 8, further comprising a visual displayconfigured to display image data based on signals from the detector, anda user interface, wherein the user interface is configured to allow auser to select the single fiducial marker from within an image on thedisplay.
 10. The system according to claim 8, wherein the detectortransport mechanism comprises a pivotable, arcuate track to which thedetector is coupled.
 11. The system according to claim 8, wherein thesupport transport mechanism is configured to allow the support to moveindependently in three orthogonal directions.
 12. A computer readablestorage medium for use with an x-ray imaging apparatus that generates athree-dimensional representation of a region of interest on a targetobject using a number of projections, the x-ray imaging apparatuscomprising: an x-ray source; a support transport mechanism that moves asupport for a region of interest and a single fiducial marker having oneor more marker elements of predetermined known geometry, thepredetermined known geometry of the single fiducial marker defining aninput parameter; an x-ray detector; detector transport mechanismconfigured to move the detector; and a motion controller connected tothe support transport mechanism and the detector transport mechanism,the motion controller configured to supply command signals to thesupport transport mechanism to move the region of interest and thesingle fiducial marker from a first position to a plurality of secondpositions corresponding to the number of projections and to supplycommand signals to the detector transport mechanism to move the detectorfrom a first detector position to a plurality of second detectorpositions corresponding to the number of projections, wherein theplurality of second positions and the plurality of second detectorpositions are intended to correspond to a plurality of desired secondpositions and desired second detector positions relative to the x-raysource, which are based on desired movement of the region of interestand the detector around the x-ray source to capture the number ofprojections, such that x-rays from the x-ray source are transmittedthrough the region of interest and the single fiducial marker to thedetector when the region of interest and single fiducial marker are inthe first position and the detector is in the first detector position,and transmitted again when the region of interest and single fiducialmarker are in one of the plurality of second positions and the detectoris in one of the plurality of second detector positions, the computerreadable storage medium holding executable instructions that, whenexecuted by a computer processor that is connected to the x-ray imagingapparatus, cause the computer processor to: request a user to select aregion of interest and select the single fiducial marker; generate afirst image of the region of interest and a first image of the singlefiducial marker in the first position and generate second images of theregion of interest and second images of the single fiducial marker ateach of the second positions based on received image data, generate anexpected second image of the single fiducial marker based on the inputparameter of the predetermined known geometry of the single fiducialmarker for each of the desired second positions, generate correctedsecond image data for the region of interest in each of the plurality ofsecond positions using a comparison of the expected second image of thesingle fiducial marker in the desired second position with the secondimage of the single fiducial marker that is generated at thecorresponding second position, to determine an image transform that mapsthe second image of the single fiducial marker to the expected secondimage of the single fiducial marker, and then apply the image transformto the second image for the region of interest, the corrected secondimage data thereby being the image that would have been generated if thesecond image of the single fiducial marker and of the region of interestwere actually generated at the desired second position and desiredsecond detector position; generate a three-dimensional representation ofthe region of interest utilizing the number of projections of the regionof interest, the number of projections being more than two, and whichinclude the first image of the single fiducial marker and of the regionof interest and the corrected second image data for each of the desiredsecond positions.
 13. The computer readable storage medium according toclaim 12, holding executable instructions that, when executed by acomputer processor connected to the x-ray imaging apparatus, controloperation of the motion controller.
 14. The computer readable storagemedium in accordance with claim 12, in combination with one or morefiducial markers suitable for placement on a electronic circuit board.